Abstract

It is shown that the action for boundary‐free incompressible fluid flow (i.e., the time‐integral of the kinetic energy of the motion) is an absolute minimum with respect to all velocity‐field transformations u→u* if u* is structured suitably in terms of u and an arbitrary solenoidal test field f. As suggested by this physical minimum principle, inequality analysis is applied to obtain an upper bound on the time derivative of the dissipation integral, from which there follow sufficient conditions for a monotone‐decreasing dissipation integral and a monotone‐decreasing global Reynolds number. The latter result provides an experimentally consistent necessary condition for passage from laminar to turbulent flow. Finally, inequality analysis is employed to derive a time‐dependent lower bound on the maximum velocity gradient in a generic boundary‐free flow of finite energy.